Real time thermal propagtors for massive gauge bosons

We derive Feynman rules for gauge theories exhibiting spontaneous symmetry breaking using the real-time formalism of finite temperature field theory. We also derive the thermal propagators where only the physical degrees of freedom are given thermal boundary conditions. We analyse the abelian Higgs model and find that these new propagators simplify the calculation of the thermal contribution to the self energy.Comment: 7 pages, late

Normal form transforms separate slow and fast modes in stochastic dynamical systems

Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from detailed microscale dynamics. We explore such coordinate transforms of stochastic differential systems when the dynamics has both slow modes and quickly decaying modes. The thrust is to derive normal forms useful for macroscopic modelling of complex stochastic microscopic systems. Thus we not only must reduce the dimensionality of the dynamics, but also endeavour to separate all slow processes from all fast time processes, both deterministic and stochastic. Quadratic stochastic effects in the fast modes contribute to the drift of the important slow modes. The results will help us accurately model, interpret and simulate multiscale stochastic systems

Intraoperative high resolution duplex imaging during carotid endarterectomy: Which abnormalities require surgical correction?

Objectives:This study evaluates high resolution, duplex ultrasound imaging for quality control of carotid endarterectomy in order to determine which technical factors were linked to residual stenosis and to define duplex criteria for reexploration.Design, material and methods:A consecutive series of 100 patients undergoing carotid endarterectomy were evaluated. Duplex imaging was performed prior to wound closure and repeated at 6–8 weeks postoperatively. Stenoses were classified as non-significant, moderate or severe based on duplex criteria. Intimal flaps, shelves, kinks, clamp damage and fronds were identified by ultrasound imaging.Results:Five moderate stenoses were noted in the proximal endarterectomy site (PES), and at follow-up three had resolved. Adherent fronds were detected in 83% of vessels and resolved in all but three cases. At the distal endarterectomy site there were 10 severe and 12 moderate stenoses. Intimal flaps were associated with an increased incidence of residual stenosis (p = 0.010).Conclusions:We conclude that severe stenoses with an intimal flap should be corrected immediately. Further data is required to establish the significance of kinks. Residual intimal flaps in the PES appear to remodel. The role of completion duplex may lie in the modification of surgical technique to eradicate anatomical and haemodynamic imperfections

SKA antenna systems; Outlook for non-astronomy applications

The globally endorsed Square Kilometre Array project primarily aims to advance high sensitivity radio astronomy using a distributed collection of radio telescope stations spiraling outward from the core along three to five arms out to 3000km. This planned highly sensitive instrument covering a frequency range from 70MHz up to 10GHz will be used as wideband, high resolution, wide observing field interferometer of which the first phase will be realized this decade. With the SKA telescope capabilities and with the underlying technologies, there are many space related applications outside the immediate radio astronomy domain. Examples are tracking space debris, precision orbit determination, simultaneous deep space tracking of multiple spacecrafts, GNSS and other ground segment applications, such as search and rescue tracking. After a brief introduction to the SKA, this paper will explore these potential application areas using the SKA based on its underlying approaches in the antenna and receiving subsystems

An optimization principle for deriving nonequilibrium statistical models of Hamiltonian dynamics

A general method for deriving closed reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. As in standard projection operator methods, a set of resolved variables is selected to capture the slow, macroscopic behavior of the system, and the family of quasi-equilibrium probability densities on phase space corresponding to these resolved variables is employed as a statistical model. The macroscopic dynamics of the mean resolved variables is determined by optimizing over paths of these probability densities. Specifically, a cost function is introduced that quantifies the lack-of-fit of such paths to the underlying microscopic dynamics; it is an ensemble-averaged, squared-norm of the residual that results from submitting a path of trial densities to the Liouville equation. The evolution of the macrostate is estimated by minimizing the time integral of the cost function. The value function for this optimization satisfies the associated Hamilton-Jacobi equation, and it determines the optimal relation between the statistical parameters and the irreversible fluxes of the resolved variables, thereby closing the reduced dynamics. The resulting equations for the macroscopic variables have the generic form of governing equations for nonequilibrium thermodynamics, and they furnish a rational extension of the classical equations of linear irreversible thermodynamics beyond the near-equilibrium regime. In particular, the value function is a thermodynamic potential that extends the classical dissipation function and supplies the nonlinear relation between thermodynamics forces and fluxes

Non-linear stability in photogravitational non-planar restricted three body problem with oblate smaller primary

We have discussed non-linear stability in photogravitational non-planar restricted three body problem with oblate smaller primary. By photogravitational we mean that both primaries are radiating. We normalised the Hamiltonian using Lie transform as in Coppola and Rand (1989). We transformed the system into Birkhoff's normal form. Lie transforms reduce the system to an equivalent simpler system which is immediately solvable. Applying Arnold's theorem, we have found non-linear stability criteria. We conclude that $L_6$ is stable. We plotted graphs for $(\omega_1, D_2).$ They are rectangular hyperbola.Comment: Accepted for publication in Astrophysics & Space Scienc

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Multiple Transitions to Chaos in a Damped Parametrically Forced Pendulum

We study bifurcations associated with stability of the lowest stationary point (SP) of a damped parametrically forced pendulum by varying $\omega_0$ (the natural frequency of the pendulum) and $A$ (the amplitude of the external driving force). As $A$ is increased, the SP will restabilize after its instability, destabilize again, and so {\it ad infinitum} for any given $\omega_0$. Its destabilizations (restabilizations) occur via alternating supercritical (subcritical) period-doubling bifurcations (PDB's) and pitchfork bifurcations, except the first destabilization at which a supercritical or subcritical bifurcation takes place depending on the value of $\omega_0$. For each case of the supercritical destabilizations, an infinite sequence of PDB's follows and leads to chaos. Consequently, an infinite series of period-doubling transitions to chaos appears with increasing $A$. The critical behaviors at the transition points are also discussed.Comment: 20 pages + 7 figures (available upon request), RevTex 3.

Initial Conditions for Models of Dynamical Systems

The long-time behaviour of many dynamical systems may be effectively predicted by a low-dimensional model that describes the evolution of a reduced set of variables. We consider the question of how to equip such a low-dimensional model with appropriate initial conditions, so that it faithfully reproduces the long-term behaviour of the original high-dimensional dynamical system. Our method involves putting the dynamical system into normal form, which not only generates the low-dimensional model, but also provides the correct initial conditions for the model. We illustrate the method with several examples. Keywords: normal form, isochrons, initialisation, centre manifoldComment: 24 pages in standard LaTeX, 66K, no figure